Sound Logical Explanations for Mean Aggregation Graph Neural Networks

TL;DR

This paper investigates the explainability and expressivity of mean aggregation graph neural networks (MAGNNs), providing logical rule characterizations, practical explanations, and demonstrating comparable or improved performance on benchmarks.

Contribution

It characterizes the class of sound logical rules for MAGNNs with non-negative weights and offers a method to generate explanations for their predictions.

Findings

Sound rules can be practically obtained for MAGNNs.

Explanations are insightful and can reveal issues in trained models.

Restricting weights to non-negative improves or maintains performance.

Abstract

Graph neural networks (GNNs) are frequently used for knowledge graph completion. Their black-box nature has motivated work that uses sound logical rules to explain predictions and characterise their expressivity. However, despite the prevalence of GNNs that use mean as an aggregation function, explainability and expressivity results are lacking for them. We consider GNNs with mean aggregation and non-negative weights (MAGNNs), proving the precise class of monotonic rules that can be sound for them, as well as providing a restricted fragment of first-order logic to explain any MAGNN prediction. Our experiments show that restricting mean-aggregation GNNs to have non-negative weights yields comparable or improved performance on standard inductive benchmarks, that sound rules are obtained in practice, that insightful explanations can be generated in practice, and that the sound rules can expose issues in the trained models.